The "Customise this page" Icon can be seen in the top-right of the Dashboard Page and once activated enables the use of adding blocks to your own personal instance on the Moodle sites Dashboard area, any blocks added by this method will not affect any other user and is a great way to test blocks without worrying about changing users dashboards.
The Button you see on the left is linked to the Dashboard and can be enabled to allow blocks editing, this means new blocks can be added to your own personal instance of the Dashboard and not affect any other user. This is also linked to the "Turn Editing On" button within Courses, this means that if you Turn the editing on you can also add blocks into Courses, whilst also enabling and disabling the "Customise this page", this 2 buttons are linked and perform the same accessibility to customisation on all sites.
The Button you see on the left is the "Add a block", this allows you to add a different assortment of blocks if the "Customise this page" button or "Turn Editing on" has been enabled from the Dashboard or within a Course. This "Add a block" button can be found within the Sliding Navigation Drawer, below the "Site Administration" Button.
(For information regarding adding and removing Blocks please refer to the "Blocks" solutions Article)
Important Note: You can alter the Dashboard layout for all users by heading to:
Site Administration > Appearance > Default Dashboard Page
This will take you to the setup page where you can make changes by adding blocks or altering where different elements sit on the page, once you are happy with the layout you can press the "Reset dashboard for all users" button to make the changes instantly updated for all users accessing the dashboard page.